log27a+log9b=72
⇒log33a+log32b=72
⇒13log3a+12log3b=72
⇒log3a1/3+log3b1/2=72
⇒log3(a1/3b1/2)=72
⇒a1/3b1/2=37/2 ...(1)
log27b+log9a=23
⇒log33b+log32a=23
⇒13log3b+12log3a=23
⇒log3b1/3+log3a1/2=23
⇒log3(b1/3a1/2)=23
⇒a1/2b1/3=32/3 ...(2)
Multiplying eqn (1) and (2), we get
a5/6b5/6=325/6
⇒(ab)5/6=325/6
⇒ab=35=243